Question

1. write down this question and your work in your math notebook. you will receive credit for completion. the factored form equation for the polynomial is missing a multiplier in the blank. what is the missing multiplier? look in your notes from chapter 3.4 on how to find the a value for a polynomial equation. f(x) = ____(x - 1)²(x + 2)(x + 3) type your final answer as a fraction.

Explanation:

Step1: Use given point (0, -1.2)

Substitute $x=0$, $f(0)=-1.2$ into $f(x)=a(x-1)^2(x+2)(x+3)$
$$-1.2 = a(0-1)^2(0+2)(0+3)$$

Step2: Simplify the right-hand side

Calculate the product of constants
$$-1.2 = a(1)(2)(3)$$
$$-1.2 = 6a$$

Step3: Solve for $a$

Divide both sides by 6, convert decimal to fraction
$$a = \frac{-1.2}{6} = \frac{-\frac{6}{5}}{6}$$
$$a = -\frac{6}{5} \times \frac{1}{6} = -\frac{1}{5}$$

Answer:

$-\frac{1}{5}$